%0 Journal Article
%T Existence of a minimizer for the quasi-relativistic Kohn-Sham model
%A Carlos Argaez
%A Michael Melgaard
%J Electronic Journal of Differential Equations
%D 2012
%I Texas State University
%X We study the standard and extended Kohn-Sham models for quasi-relativistic N-electron Coulomb systems; that is, systems where the kinetic energy of the electrons is given by the quasi-relativistic operator $$ sqrt{-alpha^{-2}Delta_{x_n}+alpha^{-4}}-alpha^{-2}. $$ For spin-unpolarized systems in the local density approximation, we prove existence of a ground state (or minimizer) provided that the total charge $Z_{ m tot}$ of K nuclei is greater than N-1 and that $Z_{ m tot}$ is smaller than a critical charge $Z_{ m c}=2 alpha^{-1} pi^{-1}$.
%K Kohn-Sham equations
%K ground state
%K variational methods
%K concentration-compactness
%K density operators
%U http://ejde.math.txstate.edu/Volumes/2012/18/abstr.html